Hi! My question(s) in the end might be silly but I am no expert on this, so here it goes: Noy-Meir (1973), Pielou (1984) and a few others have pointed to non-centered PCA being in some cases useful. They clearly explain that "it is the case" when multi-dimensional data display distinct clusters (which have zero, or near-zero, projections in some subset of the axes) and the task is (exactly) to separate this clusters among the principal components. I have done my complete work using prcomp() and tested combinations of center=FALSE/TRUE and scale=FALSE/TRUE. I would like to now check this "between-axes" vs "within-axes" heterogeneity of my data and cross-check results with the various tested PCA-versions. Is there any (official or custom) function available in R that could answer this question? Some relative/comparative (preferrable simple and intuitive) measure(s)? Something that would graphically perhaps give an indication without time-consuming clustering, sampling or whatsoever processing? Even though the above mentoined authors mention some measure for the assymetry of the yielded compoenents ( uncentered -> unipolar, centered -> bipolar) I find the concept a bit hard to understand. Isn't there a quick way (function) to just say (with numbers of plots of course) "well, it seems that the data are heterogenous looking at between- axes" or the other way around "it looks like the variables differ within, more than between"? Apologies for repeating the same question (trying to understand the problem myself). Thank you, Nikos
Estimate "between-axes" vs "within-axes heterogeneity of multivariate matrices
3 messages · Nikos Alexandris
On Wednesday 22 of December 2010 05:57:17 Nikos Alexandris wrote:
[...]
Apologies for repeating the same question (trying to understand the problem myself).
I started to get a grip on this. But anyway, my questions are actually not directly about R questions - sorry for the traffic.
This time with a more-R oriented question:
Is the mrpp {vegan} package [1] useful in trying to check, or get a clue about
the differences between- and within-axes (or variables or dimensions or
columns) of a multivariate matrix?
The description explains:
" ...(MRPP) provides a test of whether there is a significant difference
between two "or more groups of sampling units. ..."
"... difference may be one of location (differences in mean) or one of spread
(differences in within-group distance) ..."
and
"... Function mrpp operates on a data.frame matrix where rows are observations
and responses data matrix. The response(s) may be uni- or multivariate. ..."
Question: what about the observations being actually the columns? Is a simple
transposing of the matrix enough? Any other alternatives or hints?
Thak you, Nikos
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[1] <http://cc.oulu.fi/~jarioksa/softhelp/vegan/html/mrpp.html>
--%<---
Nikos:
My question(s) in the end might be silly but I am no expert on this, so here it goes: Noy-Meir (1973), Pielou (1984) and a few others have pointed to non-centered PCA being in some cases useful. They clearly explain that "it is the case" when multi-dimensional data display distinct clusters (which have zero, or near-zero, projections in some subset of the axes) and the task is (exactly) to separate this clusters among the principal components. I have done my complete work using prcomp() and tested combinations of center=FALSE/TRUE and scale=FALSE/TRUE. I would like to now check this "between-axes" vs "within-axes" heterogeneity of my data and cross-check results with the various tested PCA-versions. Is there any (official or custom) function available in R that could answer this question? Some relative/comparative (preferrable simple and intuitive) measure(s)? Something that would graphically perhaps give an indication without time-consuming clustering, sampling or whatsoever processing? Even though the above mentoined authors mention some measure for the assymetry of the yielded compoenents ( uncentered -> unipolar, centered -> bipolar) I find the concept a bit hard to understand. Isn't there a quick way (function) to just say (with numbers of plots of course) "well, it seems that the data are heterogenous looking at between- axes" or the other way around "it looks like the variables differ within, more than between"? Apologies for repeating the same question (trying to understand the problem myself). Thank you, Nikos